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The pair had slipped into Egypt via its chaotic Gaza border, and then into Israel, fulfilling the warnings of Israeli security officials of the increased risk of such attacks.

The militant Hamas group, which controls Gaza, blew holes in the border wall last month, sparking the mass movement of thousands of Palestinians into Egypt.

Yesterday three Palestinian militant groups said they had sponsored the attack, including the al-Aqsa Brigades, a group linked to the moderate Fatah faction of the Palestinian President Mahmoud Abbas.

Mr Abbas’s office condemned the attack, and Israeli officials vowed to press on with peace talks with the president.

Israeli retribution for the attack was however swift, with an Israeli air strike killing a senior Palestinian militant from the Popular Resistance Committees, a group linked to Hamas, in Gaza within two hours of the bombing.

A videotape released shortly afterwards showed one of the bombers, 20-year-old Loai al-Aghwani of Gaza City, claiming that his actions would "restore dignity to the Palestinian people".

Standing in front of an al-Aqsa Brigades banner, Aghwani appealed to Fatah and Hamas "to end internal division".

Aryeh Mekel, an Israeli Foreign ministry spokesman, said: "The Palestinian terrorist organisations have shown once again who they are and what they stand for. Just like the Kassam rocket fire on Sderot and the sniper fire on Israeli fields bordering Gaza, today’s attack deliberately targeted innocent civilians."

The Israeli defence minister, Ehud Barak, pledged to speed construction of a wall on the Israeli-Egyptian border, where barbed-wire fencing is regularly breached.

In Dimona, reports said the bomber stopped for a coffee before launching his attack.

A witness described how she had seen the second bomber attempt to detonate his suicide belt as emergency services rushed to the first explosion.

"I saw them grab him and open his jacket, and I saw his explosive belt before they shot him in the head," said Jacqueline Ganish, 58, speaking at the site of the attack, a small shopping centre. "Terrorism in Dimona? We’ve never had anything like this."

News of the bombings prompted celebratory gunfire in Gaza, and a Hamas spokesman praised the attacks, though denied any involvement.

The Popular Front for the Liberation of Palestine and the al-Aqsa Martyrs Brigades have claimed responsibility alongside the Islamic Resistance Brigades; the latter is said to be linked to another shadowy group in Gaza inspired by al-Qa’eda, the Jaysh al-Umma, or Army of the Islamic Nation."

The suicide bombings were there before the closures and the resistance used every opportunity to make these glorious acts," the Hamas spokesman, Ayman Taha, told news agencies. "They show the Palestinians can respond to the enemy and their crimes."

Mr Abbas’s Palestinian Authority said it "condemns the attack in Dimona, which targeted Israeli civilians," but also condemned an Israeli attack in the West Bank which killed two Palestinians early on Monday.

The last suicide bombing in Israel was in the southern resort town of Eilat, where Israel’s border meets Egypt and Jordan, on Jan 27, 2007.